A Crystal Plasticity Theory for Latent Hardening by Glide Twinning Through Dislocation Transmutation and Twin Accommodation Effects
El Kadiri, H., & Oppedal, A. L. (2010). A Crystal Plasticity Theory for Latent Hardening by Glide Twinning Through Dislocation Transmutation and Twin Accommodation Effects. Journal of the Mechanics and Physics of Solids. Elsevier. 58(4), 613--624.
Imagine a residual glide twin interface advancing in a grain under the action of a monotonic stress. Close to the grain boundary, the shape change caused by the twin is partly accommodated by kinks and partly by slip emissions in the parent; the process is known as accommodation effects. When reached by the twin interface, slip dislocations in the parent undergo twinning shear. The twinning shear extracts from the parent dislocation a twinning disconnection, and thereby releases a transmuted dislocation in the twin. Transmutation populates the twin with dislocations of diverse modes. If the twin deforms by double twinning, double-transmutation occurs even if the twin retwins by the same mode or detwins by a stress reversal. If the twin deforms only by slip, transmutation is single. Whether single or double, dislocation transmutation is irreversible. The multiplicity of dislocation modes increases upon strain, since the twin finds more dislocations to transmute upon further slip of the parent and further growth of the twin. Thus, the process induces an increasing latent hardening rate in the twin. Under profuse twinning conditions, typical of double-lattice structures, this rate-increasing latent hardening combined with crystal rotation to hard orientations by twinning is consistent with a regime of increasing hardening rate, known as Regime II or Regime B. In this paper, we formulate governing equation of the above transmutation and accommodation effects in a crystal plasticity framework. We use the dislocation density based model originally proposed by Beyerlein and Tomé  to derive the effect of latent hardening in a transmuting twin. The theory is expected to contribute to surmounting the difficulty that current models have to simultaneously predict under profuse twinning, the stress-strain curves, intermediate deformation textures, and intermediate twin volume fractions.